Optical solitary waves in biased photorefractive media

The purpose of this research is to systematically investigate nonlinear wave propagation in biased photorefractive crystals, with special emphasis given to optical spatial soliton states. The two types of photorefractive solitons that are possible under these conditions, i.e. quasi-steady-state and steady-state solitons, are considered in detail. The main part of this study, however, is devoted to the investigation of spatial solitons of the steady-state type, also known by now in the literature as screening solitons.; Within the context of quasi-steady-state regime, we demonstrate for the first time that a Gaussian beam can undergo spatial compression when it traverses a biased photorefractive medium. This is possible provided that the external bias field exceeds the critical value necessary to establish photorefractive spatial solitons. Beam self-deflection effects arising from the {dollar}pi{dollar}/2-phase-shifted component of the photorefractive grating are also considered.; The theory of steady-state photorefractive solitons is developed on the basis of the Kukhtarev-Vinetskii's model. The evolution equations of one-dimensional optical spatial solitons in photorefractive media are then derived. In the steady-state regime and under appropriate external bias conditions, our analysis indicates that the underlying wave equation can exhibit bright, dark as well as gray spatial soliton states. The characteristics of these self-trapped optical beams are discussed in detail. Moreover, the self-bending process of steady-state bright spatial solitons in biased photorefractive media is investigated by taking into account diffusion effects. By integrating numerically the nonlinear propagation equation, it is found that the soliton self-bending evolution is approximately adiabatic. The self-deflection process is then further studied using perturbation analysis, which predicts that the center of the optical beam moves on a parabolic trajectory and, moreover, that the central spatial frequency component shifts linearly with the propagation distance.; We also show that the vector beam evolution equations in properly oriented biased photorefractive media can exhibit bright-dark soliton pair solutions under steady-state conditions. These wave pairs are obtained perturbatively provided that the intensities of the two optical beams are approximately equal. Our analysis indicates that these bright-dark vector solitons exist irrespective of the polarity of the external bias field. The stability of these vector pairs is also considered.; Finally, the modulational instability of quasi-plane-wave optical beams in biased photorefractive media is investigated. The spatial growth rate of the sideband perturbations is obtained by globally treating the space-charge field equation. Our analysis indicates that the growth rates depend on the strength of the externally applied electric field and, moreover, on the ratio of the optical beam's intensity to that of the dark irradiance. The process of modulational instability in both the low and high spatial-frequency regimes is considered in great detail.